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Do the Math
01/06/2005 . Source: Mark R. Leeper 
A phrase you hear frequently is "do the math." The sort of thing is "One man. Three women. Do the math." Wow. Sounds impressive, huh? Usually when you hear or read that there is no mathematics whatsoever to do. Or if there is mathematics to do, it is second grade arithmetic. There is a one third of a man per woman. So what does that mean? They aren't going to divide him up. I think the phrase "do the math" should really be licensed and its usage controlled. Anyone who says to do the math should have to prove first that there is some math there to do and second that he himself can do the math. Bluffing is probably more common than bona fide cases where there is mathematics that can be done. You do see cases where the real mathematics is highly sophisticated and the person who says "do the math" has not done any himself. This is closely related to proof by intimidation. Somebody might say, "we will run out of food by the middle of this century--do the math.
Okay. So let's actually do some of the math. In Robert Heinlein's TUNNEL IN THE SKY, a story that takes place considerably in the future, there is a reference to the claim that if everybody in China was lined up four abreast and marched past a point, say a reviewing stand, the end of the line would never pass it. Chinese are born too fast. (Well, I have always heard the problem saying they were walking off a cliff, but that is needlessly gruesome. For once Heinlein is more politically correct than the norm.) Heinlein says the assertion is not true and that even if one ignores deaths it would take only about four years to review the entire Chinese population.
I do not know where Heinlein got his figures, but I went to the CIA web page that gives the population, birth rate, and death rate for China ( http://www.cia.gov/cia/publications/factbook/print/ch.html). Let's do the math. In the year 2004 there were 1.299 billion people in China. (This assumes that figure is accurate and the Chinese are not hiding from the government the number of children they have. The government punishes families with too many children, and some families really do cheat and hide the number of children they actually have.)
In 2004 there were 12.98 births per 1000 and 6.92 deaths per 1000. That is a net change of 6.06 added to the line per 1000. (I have no idea why all these figures fall so suspiciously close to nice round numbers. What are the chances? Do the math.) With 1.299 billion people that gives you an approximation of 7,817,400 people added per year. That is 21,417 people added per day. That is 892.4 people added per hour. Or 0.247888 people added per second. That is very close to 4 seconds per person. (Another nearly round number.) Or a new row of four people would be added about every 16 seconds.
So for the numbers to work and the statement to be true the row of four people walking abreast would have to pass by every 16 seconds. That is a fairly open rank. I think we picture it as being more likely a row would walk by every two seconds. So walking four abreast is not going to do it. One person walking by every 4 seconds would be about right. But this assumes that children born to parents who have already walked by would have to go through the line. Even with that assumption eventually the Chinese population would have all been reviewed.
Now Heinlein, who I suspect did not really do the mathematics, says that his high school student figured how long it would take to deplete the un-reviewed population. He came up with four years somehow. I tried the calculation and found it to be a nasty differential equation. It has been thirty-one years since I have done a really nasty differential equation. Hey, you want more drama in the MT VOID? Here it is. I am going to face my own demons right here in front of the MT VOID readership. I am going to challenge myself to solve this problem.
My own personal demon is the mathematics I have forgotten. Now I will put it to the test. Next week I am going to come back with the answer or I will admit that I am just not the sharp mathematician I used to be. I will report the results next week. I may give the solution technique if I can make it sufficiently clear, but I will come back with some sort of answer or an admission of defeat. I wonder if I can run this like a walk-a-thon. Anyone want to pledge money to Oxford Famine Relief if I am able to solve this problem? (You know, this is going to be pretty depressing if I fail. Maybe this isn't such a good idea.)
To be continued next week.
Mark R. Leeper
Copyright 2005 Mark R. Leeper
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